Cloth simulation doesn't go to Z axis
Issues with cloth simulations such as this are most commonly caused by either needing to Apply Scale, starting already intersecting with a collision mesh, Collision settings or Self Collision settings.
Things to try :

Apply Scale on all of your meshes (the cloth and any colliders)
Separate the meshes more at the start of the simulation and see if that helps avoid the erratic behaviour to rule out intersections
Adjust collision settings one at a time to see how they affect collisions
Check your normals are facing the correct direction on each of your collision meshes
Try disabling Self Collision and/or adjust each setting to see what helps

After each stage you’ll need to re-bake the animation to ensure the new state is taken into account.